The null hypothesis was that rs56372821 only affects CUD via its effect on tobacco smoking, which has an odds ratio 0.954 (TOR)30. We assumed a prevalence of CUD among tobacco users of 0.045 (CT)76 and a CUD prevalence among tobacco non-users of 0.01 (Ct)5, independently of the six groups. Given the prevalence of tobacco smoking (PRE) among one of the six groups, we could calculate the probability of tobacco smoking for minor allele carriers (Tm) and for major allele carriers (TM) among the groups, using the formulae of total probability PRE = MAF Tm + (1 - MAF)TM and odds ratio TOR = (Tm(1 - TM))/(TM(1 - Tm)). Then we simply simulated first the tobacco use status of each individual using the probabilities Tm and TM, and further the CUD status using the probabilities CT and Ct, and computed the simulated common Cochran-Mantel-Haenszel odds ratio for CUD. We did not require the total number of simulated CUD cases per stratum to match the observed numbers, because we wanted to keep this approach as elementary as possible. We repeated the simulation
